Joianna Wallace Pd:1 Extra Credit Geometry Study Guide Joianna Wallace Pd:1 Extra Credit

Types Triangle Acute Triangle Obtuse Triangle Right Triangle Scalene Triangle Isosceles Triangle Equilateral Triangle Equiangular Triangle

Acute Triangle A triangle where all three angles are less than ninety degrees

Obtuse Triangle A triangle where one of the sides is over ninety degrees

Right Triangle A triangle where one of the angles is ninety degrees Parts-Legs and hypotenuse

Scalene Triangle A triangle with no equal sides, so every side and angle is a different length

Isosceles Triangle A triangle with at least two equal sides and angles.

Equilateral Triangle A triangle in which all three sides are congruent

Equiangular Triangle A triangle where all three angles are congruent. *Note: Most equiangular triangles are equilateral.

Triangle Inequality Postulate The sum of the lengths of any two sides of a triangle must be greater than the third side

Triangle Inequality Postulate Is ABC a triangle?

Triangle Inequality Postulate AC+CB=10; 10>7; Therfore ABC is a triangle by the Triangle Inequality Postulate.

Triangle Sum Theorem The sum of the interior angles of any triangle is equal to 180 degrees

Triangle Sum Theorem Based on the Triangle Sum Theorem, what is the value of x?

Triangle Sum Theorem The Triangle Sum Theorem states all angles equal 180 degrees. Angle A plus Angle C equals 95 degrees. So by this theorem Angle B is 85 degrees.

Third Angle’s Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are also congruent

Third Angle’s Theorem Is Triangle PQR congruent to Triangle LJK?

Third Angle’s Theorem The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are congruent also.

Side Side Side Theorems If all three sides of one triangle are congruent to all three sides of a second triangle, then the two triangles are congruent

Side Angle Side Theorem If two sides and the included angle of one triangle are congruent to two sides and the included side of a second triangle, then the two triangles are congruent

Angle Side Angle Theorem If two sides and the included angle of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

Angle Angle Side Theorem If two angles and a non-included side of one triangle is congruent to two angles and a non-included side of another triangles are congruent.

Hypotenuse Leg Theorem if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

Corresponding Parts of Congruent Triangles are CPCTC Corresponding Parts of Congruent Triangles are

CPCTC Ex. Given: AC\\DB and P is the midpoint of CD Prove:   CP is congruent to DP

CPCTC Proof: Statement Reason Given Alternate interior angles are congruent   P is the midpoint of CD Definition of "midpoint" Vertical angles are congruent ASA CPCTC

Isosceles Triangle Theorem If two sides of a triangle are congruent, the angles opposite them are congruent.

Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, the sides opposite them are congruent. 

Overlapping Triangles Given: Prove:

Overlapping Triangles Given Substitution Post.